Many top sports people have had or have asthma Ian botham, Paula Radcliff and Paul Scholes to mention a few.Some claim it has improved the capacity and efficiency of their lungs.
Before i go on, much of what I may print is controversial.Before undertaking any big changes in your routine check with your docter.
We are designed to breath through our noses with the mouth as an emergency backup.It is my belief that (apart from genetic and envirometally learned allergies) many asthma sufferers have baby/childhood history of infections and breathing difficulties.This trains the body to breath inefficiently,ie via mouth and fast high in the chest.This is mild hyperventilation which can be exacerbated during exercise.The oxeygen-CO2 levels go out of normal parameters and the respiritory system goes into protect mode (producing mucous to restore CO2 balence).This can start a cycle eventually causing an attack.
Nasal breathing even at night (lightly tapeing the mouth), providing you have clear enough air flow.learning to breath using all three basic breathing methods (put you hand on what moves mouth & upper chest,mid-Chest & outer ribs and most important diaphram, as you breath in your belly goes out).
Some Practicioners advocate an increase in steroids while learning this and a decrease in inhaler use {THATS SOME NOT ME see your doc}.
The General consensus from BUTEKO METHOD to AYURVEDIC METHOD(reseach if intrested) is learning to breath well as in Yoga.
There are myriad of other tips available,conventional and non,such as a small amount of sesame oil in the nose before training.
Im worried that im not being controversial enough so I also believe allergies can be trained from the system by reeducating the Brain /body response. Past trauma can partially lock the autonomic breathing into near permanent (fight flight mode) and can also be retrained.
Hope this is of some help in letting you know there are many options and so keep on training.